We propose a model for the evolutionary ecology of words as one attempt to extend evolutionary game theory and agent-based models by utilizing the rich linguistic expressions of Large Language Models (LLMs). Our model enables the emergence and evolution of diverse and infinite options for interactions among agents. Within the population, each agent possesses a short word (or phrase) generated by an LLM and moves within a spatial environment. When agents become adjacent, the outcome of their interaction is determined by the LLM based on the relationship between their words, with the loser's word being replaced by the winner's. Word mutations, also based on LLM outputs, may occur. We conducted preliminary experiments assuming that ``strong animal species" would survive. The results showed that from an initial population consisting of well-known species, many species emerged both gradually and in a punctuated equilibrium manner. Each trial demonstrated the unique evolution of diverse populations, with one type of large species becoming dominant, such as terrestrial animals, marine life, or extinct species, which were ecologically specialized and adapted ones across diverse extreme habitats. We also conducted a long-term experiment with a large population, demonstrating the emergence and coexistence of diverse species.